Answer:
Answer of 17 is ㏒(
+15x), Answer of 33 is x = 8 , Answer of 35 is x = ㏒10/㏒2 , Answer of 37 is x = -㏒12/㏒8 and Answer of 39 is x = 5
Step-by-step explanation:
17. ㏒x + ㏒(x+15)
Using property ㏒a + ㏒b = ㏒a×b
∴ ㏒x + ㏒(x+15)
㏒x×(x+15)
㏒(+15x)
The answer is ㏒(+15x)
33. 2^(x-5) = 8
2^(x-5) = 2^3
Using property 2^a = 2^b
Then a = b
∴x-5 = 3
x = 8
The answer is x = 8
35. 2^x = 10
Taking log on both sides gives
㏒2^x = ㏒10
x×㏒2 = ㏒10
x = ㏒10/㏒2
The answer is x = ㏒10/㏒2
37. 8^-x = 12
Taking log on both sides gives
㏒8^-x = ㏒12
-x×㏒8 = ㏒12
x = -㏒12/㏒8
The answer is x = -㏒12/㏒8
39. 5(2^3 × x) = 8
5(8×x) = 8
x = 5
The answer is x=5
Answer:
Step-by-step explanation:
The systems of equations are
Let us assume the rate of the current be c
Now actual speed against the current is (15 - c)
And, the actual speed with the current is (15 + c)
Here we applied the time formula i.e. distance by speed
Also the upstream time - downstream time = 4
Now the equations are
<h2><u>Part A:</u></h2>
Let's denote no of seats in first row with r1 , second row with r2.....and so on.
r1=5
Since next row will have 10 additional row each time when we move to next row,
So,
r2=5+10=15
r3=15+10=25
<u>Using the terms r1,r2 and r3 , we can find explicit formula</u>
r1=5=5+0=5+0×10=5+(1-1)×10
r2=15=5+10=5+(2-1)×10
r3=25=5+20=5+(3-1)×10
<u>So for nth row,</u>
rn=5+(n-1)×10
Since 5=r1 and 10=common difference (d)
rn=r1+(n-1)d
Since 'a' is a convention term for 1st term,
<h3>
<u>⇒</u><u>rn=a+(n-1)d</u></h3>
which is an explicit formula to find no of seats in any given row.
<h2><u>Part B:</u></h2>
Using above explicit formula, we can calculate no of seats in 7th row,
r7=5+(7-1)×10
r7=5+(7-1)×10 =5+6×10
r7=5+(7-1)×10 =5+6×10 =65
which is the no of seats in 7th row.
Answer:
first, u need to know the formula for compound interest, which is:
where A is the final amount
P- initial amount
r- percent compounded(interest)
and
n- number of years
so
we have
3.8/100 = 0.038
1+0.038 =1.038
1.038^4 = 1.160885573136
475 * 1.160885573136 = 551.4206472396
approximately $551.42
Answer:
Step-by-step explanation:
Total cost for the three nights
Total_3 = $298.17 + 3*u
Where <em>u </em>represents the unknown fees for a single day
To find the daily cost, we divide the previous equation by three
Daily cost = ($298.17 + 3*u)/3
Daily cost = ($99.39 + u)
So, if we create an inequality for the daily cost
Let x = Daily cost
x > $99.39
She will pay more than $99.39 per night
